2025/04/05 by Fricain, Emmanuel, Sarkar, Jaydeb
#30H45 #32M15 #46E22 #47A53 #47B13 #Complex Variables (math.CV) #FOS: Mathematics #Functional Analysis (math.FA)
paper · doi:10.48550/arxiv.2504.04068
We establish a connection between the de Branges-Rovnyak spaces and the Cowen-Douglas class of operators which is associated with complex geometric structures. We prove that the backward shift operator on a de Branges-Rovnyak space never belongs to the Cowen-Douglas class when the symbol is an extreme point of the closed unit ball of H^∞ (the algebra of bounded analytic functions on the open unit disk). On the contrary, in the non extreme case, it always belongs to the Cowen-Douglas class of rank one. Additionally, we compute the curvature in this case and derive certain exotic results on unitary equivalence and angular derivatives.